Undergraduate Algebraic Geometry

Author: Miles Reid
Editor: Cambridge University Press
ISBN: 9780521356626
File Size: 80,59 MB
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This short and readable introduction to algebraic geometry will be ideal for all undergraduate mathematicians coming to the subject for the first time.

Elementary Geometry Of Algebraic Curves

Author: C. G. Gibson
Editor: Cambridge University Press
ISBN: 9780521646413
File Size: 49,42 MB
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Here is an introduction to plane algebraic curves from a geometric viewpoint, designed as a first text for undergraduates in mathematics, or for postgraduate and research workers in the engineering and physical sciences. The book is well illustrated and contains several hundred worked examples and exercises. From the familiar lines and conics of elementary geometry the reader proceeds to general curves in the real affine plane, with excursions to more general fields to illustrate applications, such as number theory. By adding points at infinity the affine plane is extended to the projective plane, yielding a natural setting for curves and providing a flood of illumination into the underlying geometry. A minimal amount of algebra leads to the famous theorem of Bezout, while the ideas of linear systems are used to discuss the classical group structure on the cubic.

Undergraduate Commutative Algebra

Author: Miles Reid
Editor: Cambridge University Press
ISBN: 9780521458894
File Size: 37,81 MB
Format: PDF
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For those looking for an introduction to the area of commutative algebra, this book opens all the right doors and provides a clarity of understanding that all will welcome.

Basic Algebraic Geometry 1

Author: Igor R. Shafarevich
Editor: Springer Science & Business Media
ISBN: 3642379567
File Size: 60,79 MB
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Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevich’s book is a must.'' The third edition, in addition to some minor corrections, now offers a new treatment of the Riemann--Roch theorem for curves, including a proof from first principles. Shafarevich's book is an attractive and accessible introduction to algebraic geometry, suitable for beginning students and nonspecialists, and the new edition is set to remain a popular introduction to the field.

An Introduction To Algebraic Geometry And Algebraic Groups

Author: Meinolf Geck
Editor: Clarendon Press
ISBN: 0191663727
File Size: 65,19 MB
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An accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic groups from first principles. Building on the background material from algebraic geometry and algebraic groups, the text provides an introduction to more advanced and specialised material. An example is the representation theory of finite groups of Lie type. The text covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, a thorough treatment of Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields. Experts in the field will enjoy some of the new approaches to classical results. The text uses algebraic groups as the main examples, including worked out examples, instructive exercises, as well as bibliographical and historical remarks.

Algebraic Geometry

Author: Solomon Lefschetz
Editor: Courier Corporation
ISBN: 0486154726
File Size: 61,34 MB
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An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.

Elementary Algebraic Geometry

Author: Klaus Hulek
Editor: American Mathematical Soc.
ISBN: 0821829521
File Size: 46,31 MB
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This book is a true introduction to the basic concepts and techniques of algebraic geometry. The language is purposefully kept on an elementary level, avoiding sheaf theory and cohomology theory. The introduction of new algebraic concepts is always motivated by a discussion of the corresponding geometric ideas. The main point of the book is to illustrate the interplay between abstract theory and specific examples. The book contains numerous problems that illustrate the general theory. The text is suitable for advanced undergraduates and beginning graduate students. It contains sufficient material for a one-semester course. The reader should be familiar with the basic concepts of modern algebra. A course in one complex variable would be helpful, but is not necessary.

Introduction To Algebraic Geometry

Author: Brendan Hassett
Editor: Cambridge University Press
ISBN: 1139464590
File Size: 39,94 MB
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Algebraic geometry, central to pure mathematics, has important applications in such fields as engineering, computer science, statistics and computational biology, which exploit the computational algorithms that the theory provides. Users get the full benefit, however, when they know something of the underlying theory, as well as basic procedures and facts. This book is a systematic introduction to the central concepts of algebraic geometry most useful for computation. Written for advanced undergraduate and graduate students in mathematics and researchers in application areas, it focuses on specific examples and restricts development of formalism to what is needed to address these examples. In particular, it introduces the notion of Gröbner bases early on and develops algorithms for almost everything covered. It is based on courses given over the past five years in a large interdisciplinary programme in computational algebraic geometry at Rice University, spanning mathematics, computer science, biomathematics and bioinformatics.

Algebraic And Analytic Geometry

Author: Amnon Neeman
Editor: Cambridge University Press
ISBN: 0521709830
File Size: 43,63 MB
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Modern introduction to algebraic geometry for undergraduates; uses analytic ideas to access algebraic theory.

Rudiments Of Algebraic Geometry

Author: W.E. Jenner
Editor: Courier Dover Publications
ISBN: 0486818063
File Size: 46,46 MB
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Aimed at advanced undergraduate students of mathematics, this concise text covers the basics of algebraic geometry. Topics include affine spaces, projective spaces, rational curves, algebraic sets with group structure, more. 1963 edition.

Introduction To Algebraic Geometry

Author: Justin Smith
Editor: Chapman and Hall/CRC
ISBN: 9781466572485
File Size: 78,20 MB
Format: PDF
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Unlike other books on algebraic geometry, this text includes applications from various areas of mathematics, biology, and physics. Designed for advanced undergraduate and graduate students with an applied mathematics background, the book develops most of the necessary commutative algebra. It describes all of the algebraic and geometric concepts required for understanding algebraic geometry. The author also presents a very recent and simpler proof of the dimension of an affine variety. A solutions manual and figure slides are available with qualifying course adoption.

Algebraic Geometry

Author: Thomas A. Garrity
Editor: American Mathematical Soc.
ISBN: 0821893963
File Size: 13,10 MB
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Algebraic Geometry has been at the center of much of mathematics for hundreds of years. It is not an easy field to break into, despite its humble beginnings in the study of circles, ellipses, hyperbolas, and parabolas. This text consists of a series of ex

Using Algebraic Geometry

Author: David A. Cox
Editor: Springer Science & Business Media
ISBN: 1475769113
File Size: 57,93 MB
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An illustration of the many uses of algebraic geometry, highlighting the more recent applications of Groebner bases and resultants. Along the way, the authors provide an introduction to some algebraic objects and techniques more advanced than typically encountered in a first course. The book is accessible to non-specialists and to readers with a diverse range of backgrounds, assuming readers know the material covered in standard undergraduate courses, including abstract algebra. But because the text is intended for beginning graduate students, it does not require graduate algebra, and in particular, does not assume that the reader is familiar with modules.

An Algebraic Approach To Geometry

Author: Francis Borceux
Editor: Springer Science & Business Media
ISBN: 3319017330
File Size: 44,35 MB
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This is a unified treatment of the various algebraic approaches to geometric spaces. The study of algebraic curves in the complex projective plane is the natural link between linear geometry at an undergraduate level and algebraic geometry at a graduate level, and it is also an important topic in geometric applications, such as cryptography. 380 years ago, the work of Fermat and Descartes led us to study geometric problems using coordinates and equations. Today, this is the most popular way of handling geometrical problems. Linear algebra provides an efficient tool for studying all the first degree (lines, planes) and second degree (ellipses, hyperboloids) geometric figures, in the affine, the Euclidean, the Hermitian and the projective contexts. But recent applications of mathematics, like cryptography, need these notions not only in real or complex cases, but also in more general settings, like in spaces constructed on finite fields. And of course, why not also turn our attention to geometric figures of higher degrees? Besides all the linear aspects of geometry in their most general setting, this book also describes useful algebraic tools for studying curves of arbitrary degree and investigates results as advanced as the Bezout theorem, the Cramer paradox, topological group of a cubic, rational curves etc. Hence the book is of interest for all those who have to teach or study linear geometry: affine, Euclidean, Hermitian, projective; it is also of great interest to those who do not want to restrict themselves to the undergraduate level of geometric figures of degree one or two.

Algorithms In Real Algebraic Geometry

Author: Saugata Basu
Editor: Springer Science & Business Media
ISBN: 3662053551
File Size: 50,51 MB
Format: PDF
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In this first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing. Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects. Researchers in computer science and engineering will find the required mathematical background. This self-contained book is accessible to graduate and undergraduate students.

Ideals Varieties And Algorithms

Author: David A Cox
Editor: Springer Science & Business Media
ISBN: 0387356509
File Size: 46,83 MB
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This book details the heart and soul of modern commutative and algebraic geometry. It covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. In addition to enhancing the text of the second edition, with over 200 pages reflecting changes to enhance clarity and correctness, this third edition of Ideals, Varieties and Algorithms includes: a significantly updated section on Maple; updated information on AXIOM, CoCoA, Macaulay 2, Magma, Mathematica and SINGULAR; and presents a shorter proof of the Extension Theorem.

Basic Algebraic Geometry 2

Author: Igor R. Shafarevich
Editor: Springer Science & Business Media
ISBN: 3642380107
File Size: 23,20 MB
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Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevich’s book is a must.'' The second volume is in two parts: Book II is a gentle cultural introduction to scheme theory, with the first aim of putting abstract algebraic varieties on a firm foundation; a second aim is to introduce Hilbert schemes and moduli spaces, that serve as parameter spaces for other geometric constructions. Book III discusses complex manifolds and their relation with algebraic varieties, Kähler geometry and Hodge theory. The final section raises an important problem in uniformising higher dimensional varieties that has been widely studied as the ``Shafarevich conjecture''. The style of Basic Algebraic Geometry 2 and its minimal prerequisites make it to a large extent independent of Basic Algebraic Geometry 1, and accessible to beginning graduate students in mathematics and in theoretical physics.

Algebraic Geometry For Beginners

Author: C. Musili
Editor: Springer
ISBN: 9386279053
File Size: 53,61 MB
Format: PDF, ePub
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Computational Algebraic Geometry

Author: HENRY SCHENCK
Editor: Cambridge University Press
ISBN: 9780521536509
File Size: 61,54 MB
Format: PDF, Kindle
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Table of contents

Computing In Algebraic Geometry

Author: Wolfram Decker
Editor: Springer Science & Business Media
ISBN: 3540289925
File Size: 29,97 MB
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This book provides a quick access to computational tools for algebraic geometry, the mathematical discipline which handles solution sets of polynomial equations. Originating from a number of intense one week schools taught by the authors, the text is designed so as to provide a step by step introduction which enables the reader to get started with his own computational experiments right away. The authors present the basic concepts and ideas in a compact way.